Marcinkiewicz integrals on product spaces

Tom 167 / 2005

H. Al-Qassem, A. Al-Salman, L. C. Cheng, Y. Pan Studia Mathematica 167 (2005), 227-234 MSC: Primary 42B20; Secondary 42B25. DOI: 10.4064/sm167-3-4

Streszczenie

We prove the $L^p$ boundedness of the Marcinkiewicz integral operators $\mu_{\mit\Omega}$ on ${\mathbb R}^{n_1}\times\cdots\times{\mathbb R}^{n_k}$ under the condition that ${\mit\Omega} \in L (\log L)^{k/2}({\mathbb S}^{n_1 -1}\times\cdots\times{\mathbb S}^{n_k-1})$. The exponent $k/2$ is the best possible. This answers an open question posed by Y. Ding.

Autorzy

  • H. Al-QassemDepartment of Mathematics
    Yarmouk University
    Irbid, Jordan
    e-mail
  • A. Al-SalmanDepartment of Mathematics
    Yarmouk University
    Irbid, Jordan
    e-mail
  • L. C. ChengDepartment of Mathematics
    Bryn Mawr College
    Bryn Mawr, PA 19010, U.S.A.
    e-mail
  • Y. PanDepartment of Mathematics
    University of Pittsburgh
    Pittsburgh, PA 15260, U.S.A.
    e-mail

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